Re: Simplify With Assumptions

*To*: mathgroup at smc.vnet.net*Subject*: [mg17963] Re: [mg17931] Simplify With Assumptions*From*: "Andrzej Kozlowski" <andrzej at tuins.ac.jp>*Date*: Mon, 7 Jun 1999 02:51:20 -0400*Sender*: owner-wri-mathgroup at wolfram.com

This is strange because it is possible to write even in mathematica 3 a version of simplify which will work with such cases. Here is an very imperfect example (not meant to be used, there is plenty wrong with it!) which illustrates the idea: In[1]:= <<Algebra`AlgebraicInequalities` In[2]:= mysimplify[Sqrt[f_],{vars__},cond_List]:= PowerExpand[Sqrt[f]]/;SemialgebraicComponents[ Append[cond, PowerExpand[Sqrt[Denominator[f]]]*PowerExpand[Sqrt[Numerator[f]]]< 0],{vars}]=={}; mysimplify[f_,{vars_},cond_List]:=Simplify[f] Now we can do not only things like: In[3]:= mysimplify[Sqrt[x^2], {x}, {x > 0}] Out[3]= x but also In[3]:= mysimplify[Sqrt[(2*t^2 + 1)^2/t^2], {t}, {t > 0}] Out[3]= 2 1 + 2 t -------- t One of the many unsatisfactory things is that In[4]:= mysimplify[Sqrt[x^2], {x}, {x < 0}] Out[4]= 2 Sqrt[x ] instead of -x, but one could obviously fix that. I can't see any obvious reason why a (much better) version has not been implemented. Perhaps Adam Strzebonski would like to comment? -- Andrzej Kozlowski Toyama International University JAPAN http://sigma.tuins.ac.jp http://eri2.tuins.ac.jp ---------- >From: "David Park" <djmp at earthlink.net> To: mathgroup at smc.vnet.net >To: mathgroup at smc.vnet.net >Subject: [mg17963] [mg17931] Simplify With Assumptions >Date: Sat, Jun 5, 1999, 3:56 PM > > Simplify with assumptions in Version 4 is not everything one might > hope. > > Simplify[Sqrt[x^2], x > 0] > x > > But > > Simplify[Sqrt[(1 + 2*t^2)^2/t^2], t > 0] > Sqrt[4 + 1/t^2 + 4*t^2] > > not > > (1 + 2*t^2)/t > > Of course we can see for ourselves and PowerExpand. Yet one would have > hoped that Mathematica would have handled this case automatically. > > David Park > djmp at earthlink.net > http://home.earthlink.net/~djmp/ > > > >